Effects of liquid velocity through the orifice. The orifice discharge coefficient also is affected by the liquid velocity through the orifice. It depends on the Reynolds number based on the orifice diameter. Most published studies on orifice flow were conducted for orifice meters . When a fluid flows through a thin-plate orifice the jet contraction amounts to about 60% of the orifice area, so orifice discharge coefficients are on the order of 0.62 at Reynolds numbers above 10,000, with a maximum of about 0.7 occurring at about a Reynolds number of 200 compared with nearly unity for venture tubes and flow nozzles. The actual coefficient also is a function of the ratio of the orifice to the pipe sizes and Reynolds number. Very little published data exist on actual orifice coefficients for distributors. In the case of a packed tower distributor the orifice is discharging into a nonrestrictive open space that can be considered an infinite pipe diameter, so Eq. 2 can be used without correction for the ratio of the orifice diameter to the pipe diameter because here the ratio is less than 0.3 .
As part of a comprehensive research program on liquid flow through distributors FRI found that even when flow through the orifice is in the fully turbulent regime the orifice coefficient isn’t constant and the liquid head above the orifice is a critical parameter in determining the orifice discharge coefficient. At sufficiently low liquid head the orifice flow becomes unstable for a number of reasons. For instance, wave action in the distributor affects the head on the orifice more at low liquid pool depths than at higher liquid head levels, as we’ve already explained. Also, when the liquid pool is too low the orifice isn’t operating as a metering orifice. In addition, FRI has determined that the discharge coefficient of a vertical orifice differs slightly from that of a horizontal orifice. Ref. 7 indicates that the orifice coefficient can be as low as 0.62 and recommends use of a coefficient of 0.707 for punched holes. A good rule of thumb is to design the liquid head at the minimum flow rate to be 2 in. or greater.
Vapor-side pressure drop across liquid distributor. This will increase the liquid head needed to deliver the design flow capacity. Because vacuum columns are sensitive to pressure drop, distributors have to be designed for minimum vapor-side pressure drop. Pressure drop through a distributor is a function of open area, so narrow–trough, high open area distributors are preferred and spray distributors maybe used (where efficiency isn’t important and liquid entrainment isn’t a concern). Thus, gravity distributor design must consider the pressure drop effect on the head requirements.
The vapor-side pressure drop, Δp, is composed of friction losses inside the vapor risers, Δpf, contraction losses in vapor entrance, Δpc, and expansion losses in vapor exit, Δpe: Δp = Δpf + Δpc + Δpe (5)
These component losses can be calculated via the following equations:
Δpf = f (L/Dh)ρvVv2 (6)
Δpc = KcρvVv2 (7)
Δpe = Ke ρvVv2 (8)
where L is the height of the distributor; Dh is the hydraulic diameter of the risers; Vv is the vapor velocity; Kcis the contraction resistance coefficient; Ke is the expansion resistance coefficient; and ρv is the vapor density. From the contraction and expansion ratios, the Kc and Ke are 0.65 and 0.35, respectively. The hydraulic diameter, Dh, determined by Eq. 8, enables the pressured drop of fluid flowing in irregularly shaped conduits and channels to be calculated as if the fluid were flowing in a round pipe: Dh = 4A/WP (9)